Self-equivalences of the derived category of Brauer tree algebras
with exceptional vertices

Alexander Zimmermann

Abstract.
Let $k$ be a field and $A$ be a Brauer tree algebra associated with
a Brauer tree with possibly non trivial exceptional vertex.
In an earlier joint paper with Rapha\"el Rouquier we studied and
defined the group $TrPic_k(\Lambda)$ of standard self-equivalences
of the derived category of a $k$-algebra $\Lambda$.
In the present note we shall determine a non trivial homomorphism
of a group slightly bigger than the pure braid group on $n+1$
strings to $TrPic_k(A)$. This is a generalization of the main result
in the joint paper with Rapha\"el Rouquier. The proof uses
the result with Rapha\"el Rouquier.